Comparison of generalized transport and Monte-Carlo models of the escape of a minor species

Abstract

In a wide variety of space physics problems (e.g. polar wind, solar wind), outflowing species pass through two different regions 1. (1) a collision-dominated region, in which hydrodynamic transport equations can be applied 2. (2) a collisionless region, where kinetic models are applicable. These two regions are separated by a transition layer where more rigorous mathematical approaches should be used. One such approach is the Monte-Carlo method. The Monte-Carlo technique uses pseudo-random numbers to simulate the diffusion of a given species under the influence of gravitational and electromagnetic forces and interparticle collisions. A second possible approach is to use generalized transport equations. The 16-moment set of transport equations, considered here, is obtained by taking moments of Boltzmann's equation, assuming that the particle distribution function is an expansion about a bi-Maxwellian with correction terms proportional to the stress and the parallel and perpendicular heat flows. The purpose of this study is not to provide a new or better description of a particular flow in space. It is, rather, to compare the Monte-Carlo and 16-moment generalized transport approaches for conditions corresponding to the transition from collision-dominated to collisionless flow and to draw conclusions about these two methods based on the results of the comparison. The 16-moment and Monte-Carlo approaches are compared for the case of a minor species diffusing through a static background. First, the problem is cast in a form which makes the description independent of the way in which the background density varies with distance. For this transformed problem, the 16-moment and Monte-Carlo models show close agreement. Then, the transformed problem is ‘mapped’ to a particular case that approximates conditions existing in the Earth's upper atmosphere. The general agreement between the Monte-Carlo and 16-moment model solutions for the mapped problem is evidence that the 16-moment formalism is capable of successfully describing transitions from collision-dominated to collisionless flow.